Free Fall Equation (Air Drag) (Q3836): Difference between revisions

Revision as of 10:26, 1 October 2024

Modeling the fall of objects by the laws of classical mechanics, including the aerodynamic drag and assuming a uniform gravitational field. Moreover, assuming the falling object to be a point mass.

Language	Label	Description	Also known as
English	Free Fall Equation (Air Drag)	Modeling the fall of objects by the laws of classical mechanics, including the aerodynamic drag and assuming a uniform gravitational field. Moreover, assuming the falling object to be a point mass.

Statements

instance of

Mathematical Formulation

0 references

defining formula

{\begin{aligned}m{\dot {v}}&=mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}

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y(t)=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)

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in defining formula

v

symbol represents

Free Fall Velocity

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m

symbol represents

Free Fall Mass

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g

symbol represents

Gravitational Acceleration

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\rho

symbol represents

Density of Air

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C_{D}

symbol represents

Drag Coefficient

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A

symbol represents

Cross Section

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v_{0}

symbol represents

Free Fall Initial Velocity

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v_{\infty }

symbol represents

Free Fall Terminal Velocity

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t

symbol represents

Time

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y

symbol represents

Free Fall Height

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y_{0}

symbol represents

Free Fall Initial Height

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community

MathModDB

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P842 (Deleted Property)

0 Property P842 not found, cannot determine the data type to use.

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Generalizes Formulation

Free Fall Equation (Vacuum)

Vanishing Air Density

\rho \rightarrow 0

Vanishing Drag Coefficient

C_{D}\rightarrow 0

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Identifiers

Wikidata QID

Q38083707

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Revision as of 10:25, 1 October 2024 Shehu (talk \| contribs) Administrators 1,037 edits ‎Changed claim: defining formula (P29): \begin{align} m\dot{v}&=&mg-\frac{1}{2}\rho C_DAv^2 \\ y(t)&=&y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right) \end{align} ← Older edit		Revision as of 10:26, 1 October 2024 Shehu (talk \| contribs) Administrators 1,037 edits ‎Changed claim: defining formula (P29): \begin{align} m\dot{v}&=mg-\frac{1}{2}\rho C_DAv^2 \\ y(t)&=y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right) \end{align} Newer edit →
Property / defining formula		Property / defining formula
	${\begin{aligned}m{\dot {v}}&=&mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=&y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}$ `\begin{align} m\dot{v}&=&mg-\frac{1}{2}\rho C_DAv^2 \\ y(t)&=&y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right) \end{align}`		${\begin{aligned}m{\dot {v}}&=mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}$ `\begin{align} m\dot{v}&=mg-\frac{1}{2}\rho C_DAv^2 \\ y(t)&=y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right) \end{align}`

Free Fall Equation (Air Drag) (Q3836): Difference between revisions

${\begin{aligned}m{\dot {v}}&=&mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=&y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}$

${\begin{aligned}m{\dot {v}}&=mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}$

Revision as of 10:26, 1 October 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

Free Fall Equation (Air Drag) (Q3836): Difference between revisions

m v ˙ = m g − 1 2 ρ C D A v 2 y ( t ) = y 0 + v 0 t − v ∞ 2 g ln ⁡ cosh ⁡ ( g t v ∞ ) {\displaystyle {\begin{aligned}m{\dot {v}}&=&mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=&y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}}

m v ˙ = m g − 1 2 ρ C D A v 2 y ( t ) = y 0 + v 0 t − v ∞ 2 g ln ⁡ cosh ⁡ ( g t v ∞ ) {\displaystyle {\begin{aligned}m{\dot {v}}&=mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}}

Revision as of 10:26, 1 October 2024

Statements

Identifiers

Sitelinks

mathematics(0 entries)

${\begin{aligned}m{\dot {v}}&=&mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=&y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}$

${\begin{aligned}m{\dot {v}}&=mg-{\frac {1}{2}}\rho C_{D}Av^{2}\\y(t)&=y_{0}+v_{0}t-{\frac {v_{\infty }^{2}}{g}}\ln \cosh \left({\frac {gt}{v_{\infty }}}\right)\end{aligned}}$